Joe has a collection of nickels and dimes that is worth $6.20. If the number of dimes was doubled and the number of nickels was decreased by 37, the value of the coins would be $8.85. How many nickels and dimes does he have?

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  1. original number of nickels : x
    original number of dimes : y
    5x + 10y = 620 or
    x + 2y = 124 (#1)

    new case:
    number of nickels : 2y
    number of dimes : x-37
    5(x-37) + 10(2y) = 885
    5x + 20y = 1070
    x + 4y = 214 (#2)
    subtract: #2 - #1
    2y = 90
    y = 45
    sub into #1
    x + 2(45) = 124
    x = 34

    He had 34 nickels and 45 dimes

    check: 34nickels + 45 dimes = 170+450 = 620
    case 2:
    90 dimes + (-3nickels) = 900 - 15 = 885

    Even though there is a mathematical solution , and the answer can be verified arithmetically, the answer
    makes no real sense
    So I would say there is no solution, and the problem as stated is flawed.

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